Challenge Math Challenge - July 2019

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The Math Challenge from July 2019 featured a variety of problems, many of which were solved by participants. Key discussions included proving inequalities involving arctangents, demonstrating the uniqueness of real roots in polynomial equations, and finding orthogonal matrices for diagonalization. Participants also explored concepts in calculus, Galois theory, and properties of cyclic subspaces. The thread highlighted collaborative problem-solving and the importance of clear mathematical communication, especially in using LaTeX for presenting solutions. Overall, the discussions emphasized both the complexity and the enjoyment of tackling challenging mathematical problems.
  • #101
fresh_42 said:
Hey, I was lazy: "<" is on the keyboard ##"\leq"## is not. These details are trivial and left to the reader ;-)
That reminds me of a statistics course lecture. The lector said something like "..and since ##f## is injective, it is invertible..". Similarly, in algebra, saying something is a subgroup of ##G## is to be read as "is an isomorphic copy of a subgroup of ##G##".
 
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  • #102
nuuskur said:
That reminds me of a statistics course lecture. The lector said something like "..and since ##f## is injective, it is invertible..". Similarly, in algebra, saying something is a subgroup of ##G## is to be read as "is an isomorphic copy of a subgroup of ##G##".
or omitting "almost everywhere" in measure theory.

I have also seen isomorphic for monomorphic (here, not in books), which I really dislike.
 

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